Dimension estimates for the boundary of planar Sobolev extension domains

DOI10.1515/acv-2021-0042OpenAlexW3215529886MaRDI QIDQ2691837

Tapio Rajala, Jyrki Takanen, Danka Lučić

Publication date: 30 March 2023

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.14213

zbMATH Keywords

Hausdorff dimensionporositySobolev extension

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Length, area, volume, other geometric measure theory (28A75)

Related Items (4)

Dimension estimate for the two-sided points of planar Sobolev extension domains ⋮ A necessary condition for Sobolev extension domains in higher dimensions ⋮ Two-sided boundary points of Sobolev extension domains on Euclidean spaces ⋮ The volume of the boundary of a Sobolev \((p,q)\)-extension domain

Cites Work

• Unnamed Item
• On dimension of porous measures
• Measure density and extendability of Sobolev functions
• Whitney cubes, p-capacity, and Minkowski content
• John disks
• Hausdorff dimension and mean porosity
• On Sobolev extension domains in \(\mathbb R^n\)
• Nonsymmetric conical upper density and 𝑘-porosity
• On the Minkowski Dimension of Strongly Porous Fractal Sets in R ⁿ
• Asymptotically sharp dimension estimates for $k$-porous sets
• Distribution of Sets and Measures Along Planes

This page was built for publication: Dimension estimates for the boundary of planar Sobolev extension domains